<p>The porous Riga sheet is utilized in cooling systems, wastewater treatment, and biomedical applications, improving heat transmission, pollutant filtering, and industrial wastewater management via Lorentz force and porosity effects. In this investigation, the Williamson non-Newtonian fluid flow over a moving porous Riga surface is examined for the interaction of thermal radiation. Moreover, the implication of Darcy dissipation and viscous dissipation are taken into account for heat transport phenomenon. Effect and application of pollutant discharge factor and activation energy in concentration equation is also taken into consideration. The governing partial differential equations are solved numerically using the shooting-based Runge–Kutta method. Through similarity transformations, these equations are converted into ordinary differential equations for further analysis. Utilizing Response Surface Methodology (RSM) grounded on the Central Composite Design (CCD) model facilitates the assessment of heat transfer rates as a function of radiation, Eckert number, and porosity behaviours. The model’s accuracy and data validation are analysed using Analysis of Variance (ANOVA). The graphical analysis depicts fluid dynamics and thermal transfer across diverse factors, as well as the response of engineering coefficients to varying situations. However, the important findings are; the fluid velocity is controlled by the enhanced non-Newtonian Williamson parameter and the augmented Eckert number due to the incorporation of dissipative heat encourages the fluid temperature significantly. Further, the heat transfer model is optimized by utilizing statistical technique for the appropriate range of the factors.</p>